Rob Bayer Math 55 Worksheet June 29, 2009 Instructions • Introduce yourselves! Despite popular belief, math is in fact a team sport! • Find some blackboard space, a piece of chalk, and decide who will be your ﬁrst scribe. • Do the problems below, having a diﬀerent person be the scribe for each one. • Try to work out the problems as a group, but feel free to ﬂag me down if you run into a wall. Functions and Sets 1. Determine whether each of the following are injections, surjections, bijections, or none of the three. (a) f : R → R ,f ( x ) = 3 x-2 (b) f : R → Z ,f ( x ) = b x c (c) f : N → N ,f ( n ) = n + 1 (d) f : R → R ,f ( x ) = x ( x-3)( x + 2) 2. Decide whether each of the following are true or false. For those that are true, prove it. For those that are false, provide a counterexample. (a) If f,g are injective, then f ◦ g is (b) If f,g are surjective, then f ◦ g is (c) If f ◦ g is injective, then f is. (d) If
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Inverse function, Surjective function, popular belief, Rob Bayer, blackboard space